We experimentally and theoretically study the interaction of broadband polychromatic laser pulses with an optically dense resonant extended medium without population inversion. Experimental (probe field-pumping beam) measurements of the transmission and amplification spectra were carried out in the plasma of a positive neon glow-discharge column containing a large number of metastable atoms. The strong coupling in the field-matter system and the collective behavior of the atomic system in a resonant field were attributable to a high (∼10¹² cm^-3) density of atoms at the lower (metastable) level of the optical transitions under consideration and to a relatively low intensity of the interacting laser beams. We observed a broadband weakening of the probe field in the absence of pumping and its strengthening in the line wings in the presence of a strong field. We develop a theoretical model for the parametric amplification of collective interactions in dense extended media based on the solution of the semiclassical Maxwell-Bloch equations for conditions under which the pumping field does not destroy the dipole interaction between atoms through probe-field photons.